In several wireless communication scenarios, the received signal at a receiver antenna can be written in the following mathematical form:r=hx+n,  (1)where r is the signal detected at the receiver antenna, h is the complex-valued channel coefficient representing the gain of the wireless channel between the transmit antenna and the receive antenna, x is the transmitted symbol, and n is the sum of the noise and, possibly, some interference. Note that equation (1) could apply without loss of generality to a frequency domain representation of the received signal (i.e., a received subcarrier or tone in the case of an orthogonal frequency division multiplexing OFDMA or single carrier frequency division multiple access SC-FDMA based system like long term evolution LTE) or could also apply to an alternative time domain representation. Without loss of generality, it is further assumed here that the channel coefficient h includes the effect of transmit power and that the mean energy associated with the transmitted symbol is 1. Typically, the channel coefficient, h, is not known to the receiver. Consequently, in order to extract the transmitted symbols (or, through further processing, the transmitted information bits), the receiver generates an estimate of the channel coefficient, h. Methods or algorithms that are used by the receiver to generate the desired channel estimate(s) affect the overall performance of the communication system. These channel estimates also constitute a requirement for the implementation of many different coherent reception techniques, such as matched filter detection, equalization, multi-antenna processing (e.g. Maximal Ratio Combining, Minimum-Mean Squared Error reception with Interference Rejection Combining, or Maximum Likelihood reception), and interference cancellation. A more accurate channel estimate enables the communication system to operate at lower Signal-to-Interference-plus-Noise Ratios (SINR), which, in turn, leads to an increase in the system's capacity and/or range.
In a commonly used method to enable the receiver to estimate the channel coefficient, the transmitter periodically transmits a sequence of reference symbols that is also known to the receiver. (The reference symbols are also referred to as pilot symbols.) For example, in 3GPP's Long Term Evolution (LTE) standard, the transmitter uses a certain number of resource elements to transmit a sequence of reference symbols in each Physical Resource Block (PRB.) A PRB comprises a fixed number to time-frequency resource elements which can be used to transmit data or reference symbols. The receiver is expected to process the received signals over these resource elements to generate an estimate of the channel for that PRB. (The channel can be assumed to be more-or-less constant over a PRB.)
A well-known method that is often used to generate channel estimates from reference symbols is known as Linear Minimum Mean Squared Error (LMMSE) estimation. Assuming that the receiver is aware of the reference symbol sequences used by the desired signal as well as a few dominant interferers, the LMMSE channel estimation method may be described below.
Let r denote the vector of signals (at a receiver antenna) received over the resource elements in a resource block that are used for reference symbol transmission by the desired transmitter (that transmits the desired signal) as well as the interfering transmitters (that transmit the interfering signals). It is assumed that the channel is more or less constant over a resource block. Then, we can write the received vector r as:r=Σk=0Khkqk+n,  (2)where the desired signal is referred to by the index k=0, and the dominant interferers (whose reference symbol sequences are known to the receiver) are referred to by indices k=1 through K. Thus, the channel coefficient for the desired signal is h0, and the reference symbol sequence used by the desired transmitter is q0; the corresponding quantities associated with the kth dominant interferer (k=1, 2, . . . , K) are hk and qk. Then the estimate of the channel coefficient hk, as determined by the LMMSE method, is given by:ĥk=wk†r, for k=0, 1, 2, . . . , K,  (3)where ĥk denotes the LMMSE estimate of the channel coefficient hk, wk is the filter vector used by the channel estimation method to generate the estimate of hk, and (.)† denotes the conjugate-transpose of the corresponding matrix or vector. The filter vector wk is given by:wk=πk[Σj=0Kπjqjqj†+σ2I]−1qk,  (4)where for j=0, 1, . . . , K, πj=E{|hj|2}, denotes the expected value (average) of the received power for signal/interferer indexed j, and σ2 is the sum of the average residual received powers that can be attributed to all interferers other than the K dominant and the thermal noise. I is an identity matrix of appropriate size. Note also that while the above description of the basic LMMSE channel estimation method was given in the context of a receiver with a single receive antenna, it can easily be applied to one with multiple antennas. For instance, a separate filter vector can be constructed using equation (4) for each antenna element and the corresponding LMMSE channel estimate can be obtained by processing the signals received at an antenna element by the corresponding filter vector in accordance with eq. (3). Those familiar with the art are well aware of such extensions.
It is clear from eq. (4) that the LMMSE channel estimation method requires knowledge of the average received powers for the desired signal as well as zero or more dominant interferers, and the average residual received power. Sometimes, estimates of these received powers are available to the receiver from some ongoing measurement process that continues alongside the main data transmission process. However, there are several scenarios where such measurements are not available so that the receiver is required to estimate these average received powers from the same resource block which contains the reference symbols that are meant to help the receiver generate channel estimates.
Assume that the received signal measurements comprise signals measured at L receiver antennas for N resource elements (or transmission symbols) constituting a resource block. M resource elements within this block of size N are used for reference (or pilot) symbols while the rest are for data symbols. Each of the desired signal transmitters and interferers transmits a distinct reference symbol sequence of length M over these M resource elements. The reference symbol sequences for different transmitters (including those that transmit desired signals and/or interferers) are distinct, but not necessarily orthogonal. Assuming that there is no other way to obtain the average power estimates for the desired signals and dominant interferers, the standard method for computing these power estimates works as described below.
For the desired signal or interferer identified by the index j, let qj denote the length-M column vector whose entries denote the reference symbols transmitted by the signal or interferer j over the M resource elements used for reference symbol transmission. Let r(l) (l=1, 2, . . . , L) denote the column vector of symbols received by the lth antenna over those M resource elements. In order to compute the average received power estimate for the signal/interferer with index j, one de-rotates the received signal vectors r(l) (l=1, 2, . . . , L) with the reference symbol vector qj for each of the L antennas, and divides the resulting (de-rotated) quantities by the square of the modulus of the reference symbol vector qj. The resulting quantities, referred to as de-rotated measurements, are denoted by (M(l))j for l=1, 2, . . . , L. In other words, (M(l))j=qj+r(l)/|qj|2 for l=1, 2, . . . , L, where qj+ denotes the conjugate transpose of the vector qj.
The standard method then computes the estimate of the average received power for signal/interferer j by averaging the absolute square of the de-rotated measurements over the L receiver antennas. In other words, γj, the estimate of the average received power for signal/interferer j is given by:γj=[|(M(1))j|2+[|(M(2))j|2+ . . . +[|(M(L))j|2]/L  (5)
This estimate is used in place of πj in equations (3) and (4) above to obtain the channel estimate. Then, using the channel estimate ĥ, the received signal may be processed to obtain the desired signal(s). For example, with reference to equation (1), the desired signal {circumflex over (x)} is given by:{circumflex over (x)}=({circumflex over (h)})*r/|ĥ|2  (1A)where (ĥ)* is the complex conjugate of ĥ, and |ĥ| is the absolute value of ĥ.
Estimates of average received powers obtained in the above described manner are often noisy, and can lead to less-than-desirable performance.